Question

solve the following systems of equations by elimination, if a solution exists. \

$$\begin{cases} 4x + 16y = 20 \\\\ 12y - 15 = -3x \\end{cases}$$

select the correct choice below and fill in any answer boxes in your choice. \bigcirc a. the solution to the system is x = \square, y = \square. (type integers or simplified fractions.) \bigcirc b. there are infinitely many solutions. \bigcirc c. there is no solution.

Explanation:

Step1: Rewrite equations in standard form

First equation: $4x + 16y = 20$
Second equation rearranged: $3x + 12y = 15$

Step2: Simplify both equations

Divide first equation by 4: $x + 4y = 5$
Divide second equation by 3: $x + 4y = 5$

Step3: Analyze the simplified equations

Both equations are identical, meaning they represent the same line, so every point on the line is a solution.

Answer:

B. There are infinitely many solutions.